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Theorem ovmpt4g 6425
Description: Value of a function given by the "maps to" notation. (This is the operation analog of fvmpt2 5963.) (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
ovmpt4g.3
Assertion
Ref Expression
ovmpt4g
Distinct variable group:   ,

Proof of Theorem ovmpt4g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elisset 3120 . . 3
2 moeq 3275 . . . . . . 7
32a1i 11 . . . . . 6
4 ovmpt4g.3 . . . . . . 7
5 df-mpt2 6301 . . . . . . 7
64, 5eqtri 2486 . . . . . 6
73, 6ovidi 6421 . . . . 5
8 eqeq2 2472 . . . . 5
97, 8mpbidi 216 . . . 4
109exlimdv 1724 . . 3
111, 10syl5 32 . 2
12113impia 1193 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818  E*wmo 2283  (class class class)co 6296  {coprab 6297  e.cmpt2 6298
This theorem is referenced by:  ovmpt2s  6426  ov2gf  6427  ovmpt2dxf  6428  ovmpt2df  6434  ofmres  6796  fnmpt2ovd  6878  mapxpen  7703  pwfseqlem2  9058  pwfseqlem3  9059  fullfunc  15275  fthfunc  15276  prfcl  15472  curf1cl  15497  curfcl  15501  hofcl  15528  gsum2d2lem  17001  gsum2d2  17002  gsumcom2  17003  dprdval  17034  dprdvalOLD  17036  dprd2d2  17093  cnmpt21  20172  cnmpt2t  20174  cnmptcom  20179  cnmpt2k  20189  xkocnv  20315  sdclem2  30235  aovmpt4g  32286  ovmpt2rdxf  32928
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301
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